The present invention relates to determining the shape and dimensions of industrial products that is of great importance in manufacturing processes. One important aspect involves reverse engineering of products in order to accurately obtain their shapes and dimensions. There exits a great variety of devices to arrive at the shape and dimensions of bodies. There is a very developed industry in the metrology area including manufacturers of high precision machines that have an annual market in billions of dollars. A prominent role is played by the CMM machines that use high precision mechanical and electronic devices and a contacting probe to provide the coordinates of a point with accuracies that can be beyond the micron. Against this background optical technologies are being developed that try to match the high precision and accuracy of CMM machines. High precision mechanical devices are replaced by sophisticated software and hardware. Optical techniques provide two advantages: the non-contact aspect and the benefits of field information rather than point information.
All the optical non contact methods of contouring involves the measurement of parallax, some times called disparity in machine vision literature. Parallax is a vector resulting from the difference of the projective coordinates of a point in the space when projected into a plane from two different points. There is a large variety of optical methods that use directly the methodology developed in aero-photogrammetry. This technology has been applied for many years to the field of aerial recognizance. It has reached a great deal of sophistication in the developed software and in the optical devices developed for short range measurements. On the other hand optical methods based on the moiré technology are very old, the first technical applications date from 1929 and their adoption by engineers from the 1940's. (See, e.g., P. Dantu, “Détermination expérimentale des flexions dans une plaque plane,” Annales des Ponts et Chaussées 1-40, 272-344 (1940), and R. Weller and B. M Sheffard, “Displacement measurement by mechanical interferometry,” Proceedings of the Society of Experimental Stress Analysis 6, 35-38 (1948). The connection between moiré and parallax measurement was pointed out for the first time by L. Pirodda, “Principi e applicazioni di un metodo fotogrammetrico basato sull' impiego del moiré,” Rivista Italiana di Ingegneria 12, 1-12 (1969)).
As far as the optical technologies are concerned a great explosion has taken place and hundred's of publications can be found in the literature. These publications are characterized by different simplifications of the basic model first suggested in Pirodda. Some times the methods are called methods base on structured light, without realizing the extensive literature that came form the 1960's moiré method developments. In spite of all these developments, very few fundamental contributions have been made that add to the body of knowledge.
It was realized for the first time that to characterize completely a surface it is necessary to project or to generate more than one system of fringes, for example two orthogonal systems of lines. (See, e.g., W Schreiber and G. Notni. “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Optical Engineering 39, 159-169 (2000), and C. Reich, R. Ritter and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Optical Engineering 39, 224-231 (2000)). This conclusion was reached on the basis of the similitude of moiré and photogrammetry. A formal derivation of this requirement was made in C. A. Sciammarella, L. Lamberti, and D. Posa, “Techniques to analyze displacements and contouring of surfaces,” Proceedings of the 2007 SEM Conference on Experimental Mechanics, St. Louis, Mo. (2006). Using differential geometry it was shown that as it is well known by mathematicians surfaces are tensor entities and in R3, surfaces are tensors of second order. Hence an orthogonal system of moiré fringes is required to obtain the information required to characterize a surface.
Although various systems have been proposed which touch upon some aspects of the above problems, they do not provide solutions to the existing limitations in providing an optical system that provides accurate information regarding the contours and/or deformation of an object. The most successful model to date in the sense of producing commercial applications is the one proposed by Takeda M, Mutch K, “Fourier transform profilometry for the automatic measurement of 3-D measurement shapes”, Applied Optics, Vol. 22, No. 24, (1983). This model gave rise to an industrial application in metrology and it was implemented in an optical device manufactured by Opton that, to this date, is the most evolved commercial firm producing non contact whole-field, 3D moiré measurement machines. This company produces four different models of moiré 3-D cameras, and three standard machines in competition with CMM machines. Opton is at the same time a producer of measuring machines and a user of them in a number of products that this company and their affiliated companies manufacture in different countries such as U.S.A, Germany, Japan, and Mexico. Takeda's 1983 model continues to be used for pattern analysis by Opton.
Effect of Modeling in the Accuracy of Contouring Moiré Methods
There are several factors that limit the accuracy that can be achieved using the moiré method of contouring. The most important factor is the model used to extract the information encoded in the pattern. Takeda's model is an approximation that does not take into account some important projective geometry, differential geometry and physical optics factors. The consequence of the model limitations in accuracy goes from the 10's to the 100's of microns, depending on the surface. Most models of moiré, published in the literature, have the same limitations.
The model adopted by Schreiber et al. address the problem of projective geometry. Their model utilizes Pirodda's approach in its most comprehensive form. Moiré is a form of photogrammetry. By inference the equation of moiré are the equations of photogrammetry converted into angular variables. The photogrammetry equations are ill conditioned, that makes computations more difficult. Sciammarella et al. adopted a different approach that addressed a particular type of problem, to find the profile of a tooth of a high precision gear. This approach starts with a rigorous result of projective geometry (viewing and projecting from infinity) and adds corrective functions for finite distances of projections and observations. The effect of physical optics on the geometrical optics is also considered. In one illustrative example, the results were compared with the results of measuring the same profile with a Zeiss CMM machine of ±1 micron for one standard deviation. Both sets of values agreed within this margin of accuracy.
Another source of uncertainty in the application of moiré methods to metrology is the quality of the patterns that can be obtained. This quality depends on the properties of the surface under measurement. Particularly difficult are highly reflecting surfaces. In order to have good contrast fringes, the surface must be a diffusive surface. The diffusivity of the surface depends on the roughness of the surface. Low roughness surfaces are highly reflecting thus they send back the light that impinges upon them in the direction of the angle of reflection. Hence the contrast of the signal will be good in the direction of reflection, but these reflections in general overwhelm the camera. If one reduces the intensity of the light then the projected signal will not be seen in the other areas of the surface.
To solve this problem Opton utilizes a commercially available white spray. This spray leaves a dust that is easily removable, but according to Opton has thicknesses that vary from 30 to 100 microns. This is of course a source of uncertainty in the measurements since the thickness of the applied coating becomes an unknown. Sciammarella et al. have utilized a thinner coatings also of a dusty nature easily removable but with thicknesses that seem not to have had an impact on the measurements because of a successful comparison of measured values with the moiré method and with a CMM machine with a ±1 micron guaranteed accuracy.
The quality of the projector is also of importance in the sense that it must produce an accurate carrier. Size and weight of the projector is of importance if a portable reading head is used in connection with applications to machines similar to CMM machines. The accuracy of the results also depends greatly on the methods used in fringe pattern analysis. Not all the patterns produced by surfaces can be analyzed by simple and fast routines. Highly sophisticate methods are needed to get accurate results from fringe patterns. The complexity of the software increases in the case of moiré contouring patterns.
Finally the information obtained is limited to a certain restricted region. Hence the sensor must be moved in the space and rotated of different angles. Somehow the information must be connected from one view to another. The CMM machines use heavy tables and sensors to relate measurements done in a position to measurements done in a different position. Many optical sensors use correlation methods to match different measurements. Correlation methods are not precise enough to guarantee high precision results. Opton machines seem to have a combination of change of coordinates equations based on certain marks made in the measured surface with conventional techniques used in CMM machines.
In summary, there is a well established moiré technology in competition with the CMM machines. Of course moiré based machines produce an amount of information that is impossible to achieve with a CMM machines. This capability has a direct impact in productivity if one considers the impact of ISO9000. By introducing the moiré method machines some inspection procedures that are made by hand can be done automatically resulting in digital data. These data can be easily compared with CAD model in a computer. 3-D data are needed for product shape modeling. This task can be accomplished with a speed that the touching machine cannot compete with. The existing moiré machines of Opton go from inspection areas of the order of 20×40 cm with a depth range of 40 cm, with accuracies of the order of 10 microns on a single view of 12 mm×14 mm and depth of ±3 mm, to machines that measure areas of the order of 3 m×1 m depth of work of 1 m. Single view of 1 m×1.135 m, with accuracy of ±500 microns and depth of view of ±50 cm.
Issues that arise in the current moiré contouring technology are summarized below:
Issues Concerning Current Moiré Technology Measuring Machines
Object issues. Quality of images, low contrast fringes, shape complexity, occlusions and shadow areas are problems associated with the object.
Fringe visibility and signal quality issues. As in any other experimental methods, the signal to noise ratio is of paramount importance. In the moiré-fringe projection method there two very important factors, one is the fringe contrast and the other is the sinusoidal shape of the fringe pattern.
Mathematical model issues. Limitations arising from the adopted model and adequate interfacing between geometric optics and physical optics.
Software issue. Software is required for data acquisition, data processing and data output. To improve the quality of the signal that contains the information, it is necessary to introduce software for the manipulation of pixel information. Data processing requires robust software for phase computation. It is also necessary to introduce phase unwrapping algorithms that can handle singular points and singular lines introduced by geometrical discontinuities in the field of view.
Limited area of observation and surface matching issues. Due to the limited area that can be viewed as well as due to occlusions and shadows different views must be matched to each other. The matching method must be as accurate as the measuring method otherwise the matching process will be the factor determining the accuracy of the method. Many of the current shadow-projection moiré methods address this problem by utilizing correlation methods as matching tools. The correlation methods yield results whose accuracy is lesser that the accuracy that can be obtained by the direct observation.
Consequently, there is a need for an optical device that addresses the following:
Issues Addressed by the Present Invention
Object issues. Perhaps one of the most limiting factors to handle diverse objects is the surface properties and its impact on the quality of the signal recorded. In this invention the problem of the quality of the signal is addressed by utilizing coherent light. In one embodiment, a solid state laser is used as the light source. Utilizing gradient optics the laser light is concentrated at a point source that illuminates a grating that produces diffraction points that illuminate the surface. By using polarization it is possible to control the balance between the reflected and the diffused light hence optimizing the contras of the dots on the black background of the inter-fringe zero intensity areas. With this method good contrast fringes are obtained in metal surfaces either coated or uncoated. Furthermore pixel intensity manipulation by software makes it feasible to get better quality signals.
Fringe visibility and signal quality issues. The sinusoidal structure of the signal is guarantied in the method and apparatus of the present invention by the coherent point source illumination. Furthermore the use of a system of orthogonal fringes allows the handling of problem areas such as those that partially obscured by shadows and by transitions between surfaces.
Mathematical model issues. The present invention implements Sciammarella's mathematically correct model that addresses all the projective and differential geometry issues and the physical optics issues. The application of this mathematical model is easily implemented on the apparatus disclosed in this invention.
Software issues. The present invention utilizes a software that addresses the following issues:                a. Distinction between regions that are convex and concave;        b. A fixed reference zero common to all observations;        c. Fringe extensions in areas where the fringes may be partially missing;        d. Transitions between surfaces; and        e. Handling singularities that prevent the unwrapping of fringes at singular point, singular lines and singular areas.        
Limited area of observation and surface matching issues. The present invention addresses these issues by representing surfaces that make up the body in one single coordinate system and applying the methods in connection between different views.